I have a question from a book.
First we subtract these two vectors \begin{align} \mathbf{r}&=x\hat{e}_x+y\hat{e}_y+z\hat{e}_z\\ \mathbf{r'}&=x'\hat{e}_x+y'\hat{e}_y+z'\hat{e}_z \end{align} so we get $$ \mathbf{R}=\mathbf{r}-\mathbf{r'}=(x-x')\hat{e}_x+(y-y')\hat{e}_y+(z-z')\hat{e}_z $$ Now, let $f$ be a scalar function of $\mathbf{R}$, such that $f(\mathbf{R})$.
$f$ is a multivariable function, right? But of which variables?
Does it mean $f(\mathbf{R})=f(x,y,z)$?
Or $f(\mathbf{R})=f(x',y',z')$?
Or maybe $f(\mathbf{R})=f(x,x',y,y',z,z')$?